TEHRAN, Iran -- Smiling and waving flags, Iranians from across the political spectrum welcomed President Hassan Rouhani home Saturday with cheers for his historic phone conversation with his American counterpart. But pockets of anger over the new contact between the two enemy nations signalled challenges ahead.

Hard-liners opposed to any improved contact with Washington made their objections clear as several dozen protesters chanting "Death to America" tried to block his motorcade in Tehran. The semiofficial Mehr news agency reported that at least one demonstrator hurled a shoe -- a common gesture of contempt in the Middle East -- in Rouhani's direction. Other reports said eggs were thrown at his car.

"Dialogue with Satan is not 'hope and prudence,"' some chanted, using the Rouhani's campaign from the June presidential election.

Rouhani supporters, meanwhile, greeted him with placards thanking him for seeking peace instead of confrontation. One banner read: "Yes to peace, no to war."

Friday's 15-minute phone call between Rouhani and U.S. President Barack Obama capped a week of drama revolving around Rouhani's participation in the annual UN meeting of world leaders.

The Iranian leader now has the difficult mission of trying to unite the country behind his outreach to ease a three-decade-long estrangement with the U.S. and move toward a possible settlement to roll back sanctions imposed over Tehran's nuclear program. The West says Iran's program aims at developing weapons technology, while Tehran says it is for peaceful purposes.

The effort appears to have the critical backing of Supreme Leader Ayatollah Ali Khamenei. But even the endorsement from Iran's most powerful figure is not enough to silence criticism of the fast-paced developments during the past days.

Alaeddin Boroujerdi, who heads the foreign policy and national security committee in parliament, was quoted by Iranian media as saying that the call showed Iran's "might." But the hard-line rajanews.com news website said there was no justification for Rouhani to talk to the "Great Satan," its term for the United States, and that the conversation was "a strange and useless step."

Rouhani has followed a policy of moderation and easing tensions with the outside world, a marked distance from the bombastic style of his predecessor Mahmoud Ahmadinejad. Rouhani says Iran is ready to provide assurances that Iran's nuclear program won't be weaponized by offering greater transparency and co-operation. He has demanded lifting of sanctions in return.

Also Saturday, the CNN website, blocked since unrest broke out in 2009 over Ahmadinejad's disputed election, was accessible Saturday in what could be a sign of gradual easing of Internet restrictions and outreach to the US. In the past, blocked websites have become available temporarily before being place again behind official firewalls.

Iran's stock exchange reacted positively to news of the phone call, with the index improving by 687 points, to 46,400 on Saturday. The rial, Iran's national currency, strengthened against the U.S. dollar as the news broke. The dollar was trading at 29,500 rials in foreign currency shops, compared to 30,200 rials on Thursday.

"Historic contact on the flight back home" was the front-page headline in the moderate Etemad daily Saturday. Arman, another newspaper, wrote: "The world was caught by surprise."

Upon returning home, Rouhani told reporters that the U.S. gave him a 2,700 year-old artifact, interpreted as a new token of friendship between the United States and Iran. The artifact had been in New York since 2003, when an art dealer smuggled it into the U.S. from Iran.

Mina Yazdi, a Tehran resident, said she was "very happy" to hear about Rouhani's phone conservation with Obama, which was organized after Rouhani's staff reached out to the White House with the proposal. The two leaders were both at the UN on Tuesday following speeches to the General Assembly, but did not meet.

"I hope that, after these talks, the economic problems of Iranians are eased," Yazdi said.

Prominent conservative figures -- including Friday prayer leaders, who are all loyal to Khamenei -- have publicly endorsed Rouhani's "heroic flexibility," citing the phrase Khamenei used last week to encourage diplomatic outreach but remain aware of the nation's strategic interests.